1. **Stating the problem:** We need to calculate the value of $$K = \frac{748.200 \times (748.200 \times 735.493 - 2 \times (735.493 \times 748.200) + 748.200 \times 760.607)}{735.493^2 - 735.493 \times 760.607}$$ 2. **Understanding the formula:** This is a fraction where the numerator and denominator involve multiplication and subtraction of decimal numbers. 3. **Calculate the numerator step-by-step:** - Calculate each product inside the parentheses: - $748.200 \times 735.493 = 550,525.5726$ - $735.493 \times 748.200 = 550,525.5726$ (same as above) - $748.200 \times 760.607 = 568,993.6074$ - Substitute these values: $$748.200 \times (550,525.5726 - 2 \times 550,525.5726 + 568,993.6074)$$ - Simplify inside the parentheses: $$550,525.5726 - 1,101,051.1452 + 568,993.6074 = 18,468.0348$$ - Multiply by 748.200: $$748.200 \times 18,468.0348 = 13,823,095.5$$ 4. **Calculate the denominator:** - Calculate each term: - $735.493^2 = 540,939.6$ - $735.493 \times 760.607 = 559,263.3$ - Subtract: $$540,939.6 - 559,263.3 = -18,323.7$$ 5. **Calculate $K$ by dividing numerator by denominator:** $$K = \frac{13,823,095.5}{-18,323.7} = -754.5$$ 6. **Final answer:** $$\boxed{K \approx -754.5}$$